Related papers: Towards Flying through Modular Forms
The research project has been made for mathematical modeling of aerospace system Space-to-Surface for avoid intercepting process by flight objects Surface-to-Air. The research has been completed and created mathematical models which used…
Drones have gained popularity in a wide range of field ranging from aerial photography, aerial mapping, and investigation of electric power lines. Every drone that we know today is carrying out some kind of control algorithm at the low…
Spatial visualization is the mental ability to imagine, transform, and manipulate the spatial characteristics of objects and actions. This intelligence is a part of human cognition where actions and perception are connected on a mental…
This paper introduces a method for learning to generate line drawings from 3D models. Our architecture incorporates a differentiable module operating on geometric features of the 3D model, and an image-based module operating on view-based…
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…
The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.
The main goal of the present research is to make a summary of analytical equations that can be found to calculate a swing-by maneuver in the three-dimensional space. Analytical equations based in the patched conics approximation are showed…
This article deals with 3-forms on 6-dimensional manifodls, the first dimension where the classification of 3-forms is not trivial. There are three classes of multisymplectic 3-forms there. We study the class which is closely related to…
Machine learning methods based on statistical principles have proven highly successful in dealing with a wide variety of data analysis and analytics tasks. Traditional data models are mostly concerned with independent identically…
Most CAD or other spatial data models, in particular boundary representation models, are called "topological" and represent spatial data by a structured collection of "topological primitives" like edges, vertices, faces, and volumes. These…
The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…
Round fold maps are smooth maps on closed manifolds which are locally represented as the product maps of Morse functions and identity maps on open disks and whose singularity is realized as concentrically embedded spheres. The author…
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…
Fold maps are smooth maps at each singular point of which it is represented as the product map of a Morse function and the identity map. Round fold maps are, in short, such maps the sets of all singular points of which are embedded…
3D morphable models (3DMMs) are a powerful tool to represent the possible shapes and appearances of an object category. Given a single test image, 3DMMs can be used to solve various tasks, such as predicting the 3D shape, pose, semantic…
We study the field of moduli of singular abelian and K3 surfaces. We discuss both the field of moduli over the CM field and over $\Q$. We also discuss non-finiteness with respect to the degree of the field of moduli. Finally, we provide an…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…
A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…